Category Archives: Czech Republic

Cryptography in the NTM (Prague)

Photography by Carlos Dorce

Photography by Carlos Dorce

I hope this is my last post about the NTM in Prague after talking about the astronomical instruments and Kircher’s Organum Mathematicum! Opposite the astronomical exhibition, there is another about secrets and adults and children can play with the cryptography (if they know the Czec language!):

Ché Guevara used a number code when communicating with Fidel Castro. He transposed each letter in the text to a number […]. He then wrote those numbers one behind the other. Below that line he wrote a second line of numbers, known only to him and Castro, which was used only once. He then added both lines, number per number, and below each set of numbers he wrote (the last digit of) the sum. This give a third line of numbers. Only that row was transmitted. When Castro subtracted the second line from the third, he had the first line as the result.

The Ché method cannot be cracked because the key (the second line of numbers) is random, as long as the message, is only used once.

One of the oldest methods for hidding a message is the Ribbon Code:

The code system of winding ribbons around a shaft was already known to the Greeks of the seventh century BC. The generals of Sparta received a staff in deep secrecy, of which the other half was kept by the magistrates of the city. Messages were written on a leather belt.

The Greek called such a stick a scytale and code experts today still use that name. The scytale is an example of a ‘transposition code’, a code in which the letters of a text are mixed up according to a specified recipe. The drawback of a scytale is that the spy can already guess from the ribbons which coding technique was used. It is then only a matter of patience to find the right diameter of the shaft. Gabrielle Petit, a heroine of the Belgian resistance during World War I, passed messages on silk ribbons, which she camouflaged as part of her clothes.

Photography by Carlos Dorce

Photography by Carlos Dorce

The Caesar code is also explained:

Photography by Carlos Dorce

Photography by Carlos Dorce

And the Mask Code:

The French cardinal Richelieu (1585-1642), a famous and powerful intrigant, fully used this technique to stay in contact with his agents and spies. They were each given a mask, to put over his letters.

In this method, you and your partner each have the same grid with holes. You write a message in the holes, and afterwards you fill in the remaining space with innocent text. This technique is known as the ‘Cardan grille’ after Girolamo Cardano, of Cardan joint fame, who invented the grille in 1550. It is very difficult to crack.

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, a space for the Enigma machine:

The Enigma was the German top coding machine during World War II. The Germans thought their messages to be uncrackable. Which would indeed have been the case, if they operators hadn’t made procedural mistakes and the British hadn’t secured a code book. The mathematical genius Alan Turing designed the first automatic calculators to do the enormous amount of computations needed to check all possibilities. It is assumed Turing and his crew shortened the war with two years.

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (map)

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Bernard Bolzano’s birthhouse

Photography by Carlos Dorce

Photography by Carlos Dorce

The Municipal Library of Prague (Marianské Square No.101) is in the same place where was Bernard Bolzano’s birthhouse. The house was detroyed but we have a photography of the main door from 1906:

The grey building is not beautiful although is full of allegories and symbols and among them we can see a ruler and a compass:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Bolzano’s birthhouse in Prague (map)

Kircher’s Organum Mathematicum

Photography by Carlos Dorce

Photography by Carlos Dorce

Yesterday I didn’t remember to show Kircher’s Organum Mathematicum:

Organum Mathematicum was invented in 1661 by the Jesuit astronomer and mathematician Athanasius Kircher. This device is a comprehensive portable encyclopedia and is designed for the following disciplines: arithmetic, geometry, fortifications, chronology, gnomonics (sundials), astronomy, astrology, steganography (encoding) and music. The case contains tables for calculations without ‘tiring the mind’. Each of the nine disciplines contains 24 flat boards of different colours, with definitions and information.

This is Athanasius Kicher:

Athanasius Kircher (1602-1680) pictured in the book Mundus Subterraneus (1664) by Cornelius Bloemart (1603-1680). Source: Wikimedia Commons

Of course, in the exhibition you can also find compasses, rules, abacus, slide rules, the Napier bones,…

Photography by Carlos Dorce

Photography by Carlos Dorce

…and calculators from the 20th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (map)

The National Technical Museum in Prague

Photography by Carlos Dorce

Photography by Carlos Dorce

This is one of the Top 10 Museums in Prague! The museum was founded in 1908 and has been in its current location since 1941. It’s a very big building and the collection exhibited is so big although the exhibition about transports is its main attraction:

Photography by Carlos Dorce

Photography by Carlos Dorce

But for me, the exhibition about Astronomy has been the interesting part of the museum and I have been able to visit it on my own meanwhile my children were playing in another room with some technical toys. The astronomical rooms are very dark so it has been very difficult to take good pictures although I’ve tried to do my best. The collections has sundials, armilar spheres, quadrants, astrolabes,… and a lot of other astronomical instruments:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, the polyhedrical sundials are so beautiful like this constructed on a cube by German David Beringer around 1750:

Photography by Carlos Dorce

Photography by Carlos Dorce

Or… what about this other constructed by Mathias Karl Krausler in 1691?

Photography by Carlos Dorce

Photography by Carlos Dorce

The oldest exhibited astrolabe is this unsigned one from around 1450:

Photography by Carlos Dorce

Photography by Carlos Dorce

And there also is an unsigned torquetum from the late 16th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

One of the instruments which have surprised me has been Joost Bürgi’s sextant for measuring the angles of celestial bodies (I knew that Bürgi, one of the inventor of logarithms, had constructed a lot of clocks and astronomical instruments but I didn’t expect to find one here!). Kepler used it to measure two consecutive oppositions of the planet Mars in 1602 and 1604.

There also is Habermel’s sextant, built by Erasmus Habermel (1538 – 15th of November of 1606 in Prag) who was  mechanic at the court of Emperor Rudolph II:

Photography by Carlos Dorce

Photography by Carlos Dorce

The prevailing opinion for a long time was that the instrument belonged to Brahe and so it was called the “Tychonian sextant”.

Habermel was specialised in small devices and portable sundials and one example is this sundial in the form of a book (c.1600)…

Photography by Carlos Dorce

Photography by Carlos Dorce

… and another is this equinoctial sundial (1585):

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, look at this armilar sphere from the second half of the 16th century! It’s a piece of art!

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (map)

Brahe and Kepler together near Saint Vitus

Photography by Carlos Dorce

Photography by Carlos Dorce

Almost nobody knows that near St. Vitus Cathedral there is this wonderful sculpture representing these two great astronomers together looking at the sky. Everybody visit the cathedral, the castle and Loreto and if they walked a little bit more they’d arrive to a high school called Johannes Kepler where they’d find these two statues by Josef Vajce in 1983.

Photography by Carlos Dorce

Photography by Carlos Dorce

By the way, it seems that it’s forbidden to climb on the pedestal because two policemen had come to me and… nothing important. But it’s forbidden.

Photography by Carlos Dorce

Photography by Cristina Martínez

Location: Gimnasium Jana Keplera (map)

Tycho Brahe’s tomb

Photography by Carlos Dorce

Photography by Carlos Dorce

Today is my birthday and among all the possible mathematical posts that I can write I’ve decided to show Tycho Brahe’s tomb. I don’t know the reason but I feel good when I am in front of the tomb of one of the great scientifics! It’s like being with them and their works. I often read about their lifes and their tombs are another section of the stories which explain their fortune, jobs,…

Today Tycho Brahe has been the guest star in Prague. I had been here twice before but I hadn’t never visited the Church of Our Lady before Tyn where Brahe was buried.

Photography by Carlos Dorce

Photography by Carlos Dorce

The legend says that on October 13, 1601, Tycho Brahe attended a banquet where he drank a lot and he was so polite to leave the table to empty his bladder. So he became ill and suffered from fever, delirious and periods of unconsciousness until his death on the 24th October.

He was buried near the altar of Our Lady before Tyn where a marble monument was erected in 1604, the same year in which his wife Kirsten Jörgensdatter died and was buried next to him.

Photography by Carlos Dorce

Photography by Carlos Dorce

When the tomb was opened in 1901, the scientist thought that Brahe had been poissoned from the high level of mercury which they found in his hair. In 2010 the tomb was re-opened and new investigations demonstrated that this level of mercury wasn’t able to kill him so it’s impossible to know how Tycho Brahe died.

Thus, if you visit Prague you must go to this emblematic church of the city to see the tombstone and imagine how this great astronomer died. One thing more, Brahe had a silver prothesys in his nose because he was hurt in a duel when he was young but this interesting historical piece hadn’t been found.

Photography by Carlos Dorce

Photography by Carlos Dorce

Here you have a drawing by Josef Carmine of Our Lady before Tyn at the end of the 18th century:

Old Town Square and the Church of Our Lady before Tyn, around 1780

Old Town Square and the Church of Our Lady before Tyn, around 1780

Location: Church of Our Lady before Tyn (map)

Prague astronomical clock

Photography by Carlos Dorce

Photography by Carlos Dorce

This emblematic astronomical clock was first installed in 1410 and it’s the oldest one still working in the World. It’s mounted on the southern wall of the Old Town City Hall and it’s composed of an astronomical dial which represents the position of the Moon and the Sun in the sky and in other celestial coordinates…

Photography by Carlos Dorce

Photography by Carlos Dorce

…, the “Walk of the Apostles” over it which shows the figures of the Apostles walking in circles each hour while a skeleton representing the Death moves a rope connected to the clock’s bell:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, there is a calendar dial with medallions representing the twelve months:

Photography by Carlos Dorce

Photography by Carlos Dorce

Detail of the dial. Photography by Carlos Dorce

Detail of the dial.
Photography by Carlos Dorce

The clock was made by the imperial clockmaker Mikuláš of Kadaň and the professor Jan Šindel who taught mathematics and astronomy at Charles University in Prague in times of the Emperor Wenceslav IV of Bohemia (emperor from 1376 to 1419). Nowadays, all the people who visit Prague go to the clock to take pictures of it and to see the short Walk of the Apostles in the tower of the Old Town City Hall:

Photography by Carlos Dorce

Photography by Carlos Dorce

The clock has always been the centre of attraction of this great square as we can see from some ancient pictures. For example, here you have the clock in a drawing by Jan Josef Dietzler from 1743:

a01

View of the Old Town Hall, 1743

And this other picture also by Dietzler:

a03

View of the New Town Hall, 1743

From 1791 we have this picture by Kaspar Pluth:

a04

Coronation procession of Leopold II at Old Town Square in 1791

So in 1790 the new emperor decided to parade in front of this astronomical clock.

Holy Roman Emperor Leopold II (emperor from 1790 to 1792) Heinrich Füger (c.1790). National Gallery in Prague

Finally, we have this photography taken around 1870:

a02

View of the Old Town Hall, around 1870

Location: Prague astronomical clock (map)

Bolzano’s house in Prague

Photography by Carlos Dorce

Photography by Carlos Dorce

I have arrived at Prague this morning and after leaving my luggage in the apartment I’ve gone for a walk. Prague is very beautiful! I know that I am going to have a lot of work because mathematics and astronomy were very important here in times of the Holy Roman Emperor Rudolph II (1576–1612) when Tycho Brahe and Johannes Kepler lived in this city but Bernard Bolzano (Prague, October 5, 1781 – Prague, December 18, 1848) has been the first mathematician who has appeared to me.

Source: Wikimedia Commons

Berard Bolzano and his brother lived in this house which belonged to their parents (25 Celetná Street):

Photography by Carlos Dorce

Photography by Carlos Dorce

His house of birth doesn’t exist. He was student in the Piarist Gymnasium between 1791 and 1796 when he entered the philosophical faculty at Charles University to stydy physics, philosophy and mathematics. Tus it was in this house where Bolzano lived when he began to study mathematics and we must remember the value of Bolzano’s works in this science.

So, welcome to Prague!

Location: Bolzano’s house in Prague (map)